{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "2d7a6dde",
   "metadata": {},
   "source": [
    "# 描述性统计"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d2e44502",
   "metadata": {},
   "source": [
    "**两个描述性统计的Python工具**\n",
    "\n",
    "**PANDAS & NumPy和SciPy**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "id": "7864365d",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np \n",
    "import pandas as pd \n",
    "# 导入数据处理最重要的两个模块\n",
    "import scipy.stats as stats \n",
    "# 导入统计模块\n",
    "import scipy\n",
    "import pymysql  \n",
    "# 导入数据库模块\n",
    "\n",
    "from datetime import datetime # 时间模块\n",
    "import statsmodels.formula.api as smf  \n",
    "# OLS regression表明该模块可用于普通最小二乘法（OLS）回归分析，一种常用的线性回归方法\n",
    "\n",
    "import pyreadr # read RDS file \n",
    "#导入pyreadr库，用于读取R语言的RDS格式文件\n",
    "\n",
    "from matplotlib import style\n",
    "# 设置绘图的风格样式\n",
    "import matplotlib.pyplot as plt  \n",
    "# 导入matplotlib的pyplot子模块并别名化为plt，这是matplotlib中用于绘制各类图表的核心接口。\n",
    "import matplotlib.dates as mdates\n",
    "# 用于处理日期时间格式的数据在图表中的展示\n",
    "\n",
    "from matplotlib.font_manager import FontProperties \n",
    "# 用于在绘图时设置中文字体，解决中文显示乱码的问题\n",
    "from pylab import mpl\n",
    "# 从pylab中导入mpl，mpl可用于调整绘图的参数\n",
    "\n",
    "#mpl.rcParams['font.sans-serif'] = ['SimHei']  \n",
    "# 设置绘图语言为中文字体“黑体”\n",
    "#plt.rcParams['font.family'] = 'Times New Roman'\n",
    "# 设置绘图字体为 “Times New Roman”\n",
    "\n",
    "\n",
    "#输出矢量图 渲染矢量图\n",
    "\n",
    "%matplotlib inline\n",
    "\n",
    "#IPython 魔法命令，用于在 Jupyter Notebook 中内嵌显示matplotlib绘制的图表\n",
    "\n",
    "%config InlineBackend.figure_format = 'svg'\n",
    "\n",
    "#设置内嵌图表的格式为SVG，使图表在缩放时不会失真，适用于需要高质量图像的场景。\n",
    "\n",
    "from IPython.core.interactiveshell import InteractiveShell\n",
    "InteractiveShell.ast_node_interactivity = 'all'\n",
    "#显示每一个运行结果\n",
    "\n",
    "#设置行不限制数量\n",
    "#pd.set_option('display.max_rows',None)\n",
    "\n",
    "#设置列不限制数量\n",
    "pd.set_option('display.max_columns', None)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b98983ba",
   "metadata": {},
   "source": [
    "**下面是一段基于Pandas库用于数据读取和预处理的 Python 代码**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "id": "ff4eaabe",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
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       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Preclose</th>\n",
       "      <th>Open</th>\n",
       "      <th>Highest</th>\n",
       "      <th>Lowest</th>\n",
       "      <th>Close</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Day</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1990-12-19</th>\n",
       "      <td></td>\n",
       "      <td>96.050</td>\n",
       "      <td>99.980</td>\n",
       "      <td>95.790</td>\n",
       "      <td>99.980</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1990-12-20</th>\n",
       "      <td>99.98</td>\n",
       "      <td>104.300</td>\n",
       "      <td>104.390</td>\n",
       "      <td>99.980</td>\n",
       "      <td>104.390</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1990-12-21</th>\n",
       "      <td>104.39</td>\n",
       "      <td>109.070</td>\n",
       "      <td>109.130</td>\n",
       "      <td>103.730</td>\n",
       "      <td>109.130</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1990-12-24</th>\n",
       "      <td>109.13</td>\n",
       "      <td>113.570</td>\n",
       "      <td>114.550</td>\n",
       "      <td>109.130</td>\n",
       "      <td>114.550</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1990-12-25</th>\n",
       "      <td>114.55</td>\n",
       "      <td>120.090</td>\n",
       "      <td>120.250</td>\n",
       "      <td>114.550</td>\n",
       "      <td>120.250</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2025-08-25</th>\n",
       "      <td>3825.759</td>\n",
       "      <td>3848.163</td>\n",
       "      <td>3883.562</td>\n",
       "      <td>3839.972</td>\n",
       "      <td>3883.562</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2025-08-26</th>\n",
       "      <td>3883.562</td>\n",
       "      <td>3871.471</td>\n",
       "      <td>3888.599</td>\n",
       "      <td>3859.758</td>\n",
       "      <td>3868.382</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2025-08-27</th>\n",
       "      <td>3868.382</td>\n",
       "      <td>3869.612</td>\n",
       "      <td>3887.198</td>\n",
       "      <td>3800.350</td>\n",
       "      <td>3800.350</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2025-08-28</th>\n",
       "      <td>3800.35</td>\n",
       "      <td>3796.711</td>\n",
       "      <td>3845.087</td>\n",
       "      <td>3761.422</td>\n",
       "      <td>3843.597</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2025-08-29</th>\n",
       "      <td>3843.597</td>\n",
       "      <td>3842.823</td>\n",
       "      <td>3867.606</td>\n",
       "      <td>3839.206</td>\n",
       "      <td>3857.927</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>8473 rows × 5 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "            Preclose      Open   Highest    Lowest     Close\n",
       "Day                                                         \n",
       "1990-12-19              96.050    99.980    95.790    99.980\n",
       "1990-12-20     99.98   104.300   104.390    99.980   104.390\n",
       "1990-12-21    104.39   109.070   109.130   103.730   109.130\n",
       "1990-12-24    109.13   113.570   114.550   109.130   114.550\n",
       "1990-12-25    114.55   120.090   120.250   114.550   120.250\n",
       "...              ...       ...       ...       ...       ...\n",
       "2025-08-25  3825.759  3848.163  3883.562  3839.972  3883.562\n",
       "2025-08-26  3883.562  3871.471  3888.599  3859.758  3868.382\n",
       "2025-08-27  3868.382  3869.612  3887.198  3800.350  3800.350\n",
       "2025-08-28   3800.35  3796.711  3845.087  3761.422  3843.597\n",
       "2025-08-29  3843.597  3842.823  3867.606  3839.206  3857.927\n",
       "\n",
       "[8473 rows x 5 columns]"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data = pd.read_csv('数据000001.csv') \n",
    "# 通过 Pandas 的read_csv函数读取数据文件，将其存入data变量\n",
    "data['Day'] = pd.to_datetime(data['Day'],format='%Y/%m/%d')\n",
    "# 转化日期格式\n",
    "data.set_index('Day', inplace = True)\n",
    "# 转换后的Day列设置为数据的索引，“inplace=True” 表示在原数据上直接修改，不生成新对象\n",
    "data.sort_values(by = ['Day'], ascending=True)\n",
    "# 按照Day列对数据进行升序排序，使数据按时间先后顺序排列"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "53a8a558",
   "metadata": {},
   "source": [
    "**下面是一段基于Pandas库用于金融数据预处理和收益率计算的 Python 代码**"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2879d08a",
   "metadata": {},
   "source": [
    "·计算日收益率"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "id": "cac62662",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
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       "\n",
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       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Preclose</th>\n",
       "      <th>Open</th>\n",
       "      <th>Highest</th>\n",
       "      <th>Lowest</th>\n",
       "      <th>Close</th>\n",
       "      <th>Raw_return</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Day</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1995-01-03</th>\n",
       "      <td>647.870</td>\n",
       "      <td>637.720</td>\n",
       "      <td>647.710</td>\n",
       "      <td>630.530</td>\n",
       "      <td>639.880</td>\n",
       "      <td>-0.012333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1995-01-04</th>\n",
       "      <td>639.880</td>\n",
       "      <td>641.900</td>\n",
       "      <td>655.510</td>\n",
       "      <td>638.860</td>\n",
       "      <td>653.810</td>\n",
       "      <td>0.021770</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1995-01-05</th>\n",
       "      <td>653.810</td>\n",
       "      <td>655.380</td>\n",
       "      <td>657.520</td>\n",
       "      <td>645.810</td>\n",
       "      <td>646.890</td>\n",
       "      <td>-0.010584</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1995-01-06</th>\n",
       "      <td>646.890</td>\n",
       "      <td>642.750</td>\n",
       "      <td>643.890</td>\n",
       "      <td>636.330</td>\n",
       "      <td>640.760</td>\n",
       "      <td>-0.009476</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1995-01-09</th>\n",
       "      <td>640.760</td>\n",
       "      <td>637.520</td>\n",
       "      <td>637.550</td>\n",
       "      <td>625.040</td>\n",
       "      <td>626.000</td>\n",
       "      <td>-0.023035</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-09-24</th>\n",
       "      <td>2748.918</td>\n",
       "      <td>2770.754</td>\n",
       "      <td>2863.152</td>\n",
       "      <td>2761.372</td>\n",
       "      <td>2863.126</td>\n",
       "      <td>0.041547</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-09-25</th>\n",
       "      <td>2863.126</td>\n",
       "      <td>2901.419</td>\n",
       "      <td>2952.451</td>\n",
       "      <td>2889.048</td>\n",
       "      <td>2896.306</td>\n",
       "      <td>0.011589</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-09-26</th>\n",
       "      <td>2896.306</td>\n",
       "      <td>2893.745</td>\n",
       "      <td>3000.953</td>\n",
       "      <td>2889.014</td>\n",
       "      <td>3000.953</td>\n",
       "      <td>0.036131</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-09-27</th>\n",
       "      <td>3000.953</td>\n",
       "      <td>3049.103</td>\n",
       "      <td>3087.529</td>\n",
       "      <td>3017.445</td>\n",
       "      <td>3087.529</td>\n",
       "      <td>0.028850</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-09-30</th>\n",
       "      <td>3087.529</td>\n",
       "      <td>3194.722</td>\n",
       "      <td>3358.588</td>\n",
       "      <td>3153.697</td>\n",
       "      <td>3336.497</td>\n",
       "      <td>0.080637</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>7223 rows × 6 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "            Preclose      Open   Highest    Lowest     Close  Raw_return\n",
       "Day                                                                     \n",
       "1995-01-03   647.870   637.720   647.710   630.530   639.880   -0.012333\n",
       "1995-01-04   639.880   641.900   655.510   638.860   653.810    0.021770\n",
       "1995-01-05   653.810   655.380   657.520   645.810   646.890   -0.010584\n",
       "1995-01-06   646.890   642.750   643.890   636.330   640.760   -0.009476\n",
       "1995-01-09   640.760   637.520   637.550   625.040   626.000   -0.023035\n",
       "...              ...       ...       ...       ...       ...         ...\n",
       "2024-09-24  2748.918  2770.754  2863.152  2761.372  2863.126    0.041547\n",
       "2024-09-25  2863.126  2901.419  2952.451  2889.048  2896.306    0.011589\n",
       "2024-09-26  2896.306  2893.745  3000.953  2889.014  3000.953    0.036131\n",
       "2024-09-27  3000.953  3049.103  3087.529  3017.445  3087.529    0.028850\n",
       "2024-09-30  3087.529  3194.722  3358.588  3153.697  3336.497    0.080637\n",
       "\n",
       "[7223 rows x 6 columns]"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data_new = data['1995-01':'2024-09'].copy()\n",
    "# 对原始数据选取1995年1月至2024年9月的区间数据，并copy生成新的数据集data_new，避免后续操作对原数据的影响\n",
    "data_new['Close'] = pd.to_numeric(data_new['Close'])\n",
    "# 将data_new中 “Close” 列转换为数值类型。\n",
    "data_new['Preclose'] = pd.to_numeric(data_new['Preclose'])\n",
    "# 将 “Preclose” 列转换为数值类型.\n",
    "# 计算000001上证指数日收益率\n",
    "data_new['Raw_return'] = data_new['Close'] / data_new['Preclose'] - 1\n",
    "# 第一种：通过 “当日收盘价/前收盘价-1”的公式计算原始日收益率\n",
    "data_new"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c8c3a45e",
   "metadata": {},
   "source": [
    "·计算月度收益率"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "id": "2f6dd979",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
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       "\n",
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       "\n",
       "    .dataframe thead th {\n",
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       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Raw_return</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Day</th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1995-01-31</th>\n",
       "      <td>-0.131631</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1995-02-28</th>\n",
       "      <td>-0.023694</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1995-03-31</th>\n",
       "      <td>0.177803</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1995-04-30</th>\n",
       "      <td>-0.103552</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1995-05-31</th>\n",
       "      <td>0.207922</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-05-31</th>\n",
       "      <td>-0.005801</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-06-30</th>\n",
       "      <td>-0.038684</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-07-31</th>\n",
       "      <td>-0.009656</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-08-31</th>\n",
       "      <td>-0.032849</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-09-30</th>\n",
       "      <td>0.173908</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>357 rows × 1 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "            Raw_return\n",
       "Day                   \n",
       "1995-01-31   -0.131631\n",
       "1995-02-28   -0.023694\n",
       "1995-03-31    0.177803\n",
       "1995-04-30   -0.103552\n",
       "1995-05-31    0.207922\n",
       "...                ...\n",
       "2024-05-31   -0.005801\n",
       "2024-06-30   -0.038684\n",
       "2024-07-31   -0.009656\n",
       "2024-08-31   -0.032849\n",
       "2024-09-30    0.173908\n",
       "\n",
       "[357 rows x 1 columns]"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Month_data = data_new.resample('ME')['Raw_return'].apply(lambda x: (1+x).prod()-1).to_frame()\n",
    "# \"resample('ME')\"：对data_new按“Month End）”进行重采样，将日度数据聚合为月度数据。\n",
    "# “['Raw_return']”：选取“Raw_return”列进行计算。\n",
    "# 通过匿名函数计算月度收益率，标准公式为“（1+日收益率）的连乘积-1”，能准确反映资产在一个月内的累计收益。\n",
    "# “.to_frame()”：将计算结果转换为 DataFrame 格式，便于后续分析和查看。\n",
    "Month_data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "id": "53057f48",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
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       "      <th></th>\n",
       "      <th>Raw_return</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Day</th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1995-01-31</th>\n",
       "      <td>-0.131631</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1995-02-28</th>\n",
       "      <td>-0.023694</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1995-03-31</th>\n",
       "      <td>0.177803</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1995-04-30</th>\n",
       "      <td>-0.103552</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1995-05-31</th>\n",
       "      <td>0.207922</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-05-31</th>\n",
       "      <td>-0.005801</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-06-30</th>\n",
       "      <td>-0.038684</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-07-31</th>\n",
       "      <td>-0.009656</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-08-31</th>\n",
       "      <td>-0.032849</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-09-30</th>\n",
       "      <td>0.173908</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>357 rows × 1 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "            Raw_return\n",
       "Day                   \n",
       "1995-01-31   -0.131631\n",
       "1995-02-28   -0.023694\n",
       "1995-03-31    0.177803\n",
       "1995-04-30   -0.103552\n",
       "1995-05-31    0.207922\n",
       "...                ...\n",
       "2024-05-31   -0.005801\n",
       "2024-06-30   -0.038684\n",
       "2024-07-31   -0.009656\n",
       "2024-08-31   -0.032849\n",
       "2024-09-30    0.173908\n",
       "\n",
       "[357 rows x 1 columns]"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Month_data = data_new.resample('ME')['Raw_return'].apply(lambda x: np.prod(1+x)-1).to_frame()\n",
    "# apply(lambda x: np.prod(1+x)-1)：匿名函数结合 NumPy 的prod函数计算月度收益率，公式为 “（1+日收益率）的连乘积-1”。。\n",
    "# 使用np.prod相比Pandas内置的prod在大规模数据计算时性能更优。\n",
    "Month_data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "id": "1ce571d7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "      <th>Raw_return</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Day</th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1995-01-31</th>\n",
       "      <td>-0.131631</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1995-02-28</th>\n",
       "      <td>-0.023694</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1995-03-31</th>\n",
       "      <td>0.177803</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1995-04-30</th>\n",
       "      <td>-0.103552</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1995-05-31</th>\n",
       "      <td>0.207922</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-05-31</th>\n",
       "      <td>-0.005801</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-06-30</th>\n",
       "      <td>-0.038684</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-07-31</th>\n",
       "      <td>-0.009656</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-08-31</th>\n",
       "      <td>-0.032849</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-09-30</th>\n",
       "      <td>0.173908</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>357 rows × 1 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "            Raw_return\n",
       "Day                   \n",
       "1995-01-31   -0.131631\n",
       "1995-02-28   -0.023694\n",
       "1995-03-31    0.177803\n",
       "1995-04-30   -0.103552\n",
       "1995-05-31    0.207922\n",
       "...                ...\n",
       "2024-05-31   -0.005801\n",
       "2024-06-30   -0.038684\n",
       "2024-07-31   -0.009656\n",
       "2024-08-31   -0.032849\n",
       "2024-09-30    0.173908\n",
       "\n",
       "[357 rows x 1 columns]"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Month_data = data_new.resample('ME')['Raw_return'].apply(lambda x: np.prod(1+x)-1).to_frame()\n",
    "# 匿名函数结合NumPy的prod函数计算月度收益率，公式为 “（1+日收益率）的连乘积-1”\n",
    "# 使用np.prod在大规模数据计算时性能更优\n",
    "Month_data"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c281f152",
   "metadata": {},
   "source": [
    "·计算季度收益率"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "id": "76ac7436",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Raw_return</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Day</th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1995-03-31</th>\n",
       "      <td>-0.001466</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1995-06-30</th>\n",
       "      <td>-0.025258</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1995-09-30</th>\n",
       "      <td>0.145660</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1995-12-31</th>\n",
       "      <td>-0.231358</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1996-03-31</th>\n",
       "      <td>0.001981</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2023-09-30</th>\n",
       "      <td>-0.028603</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2023-12-31</th>\n",
       "      <td>-0.043575</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-03-31</th>\n",
       "      <td>0.022263</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-06-30</th>\n",
       "      <td>-0.024255</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-09-30</th>\n",
       "      <td>0.124383</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>119 rows × 1 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "            Raw_return\n",
       "Day                   \n",
       "1995-03-31   -0.001466\n",
       "1995-06-30   -0.025258\n",
       "1995-09-30    0.145660\n",
       "1995-12-31   -0.231358\n",
       "1996-03-31    0.001981\n",
       "...                ...\n",
       "2023-09-30   -0.028603\n",
       "2023-12-31   -0.043575\n",
       "2024-03-31    0.022263\n",
       "2024-06-30   -0.024255\n",
       "2024-09-30    0.124383\n",
       "\n",
       "[119 rows x 1 columns]"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Quarter_data = data_new.resample('QE')['Raw_return'].apply(lambda x: np.prod(1+x)-1).to_frame()\n",
    "Quarter_data"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2355bb69",
   "metadata": {},
   "source": [
    "·计算年度收益率"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "id": "672f8ccd",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Raw_return</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Day</th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1995-12-31</th>\n",
       "      <td>-0.142899</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1996-12-31</th>\n",
       "      <td>0.651425</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1997-12-31</th>\n",
       "      <td>0.302153</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1998-12-31</th>\n",
       "      <td>-0.039695</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1999-12-31</th>\n",
       "      <td>0.191750</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2000-12-31</th>\n",
       "      <td>0.517277</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2001-12-31</th>\n",
       "      <td>-0.206180</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2002-12-31</th>\n",
       "      <td>-0.175167</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2003-12-31</th>\n",
       "      <td>0.102670</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2004-12-31</th>\n",
       "      <td>-0.153997</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2005-12-31</th>\n",
       "      <td>-0.083253</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2006-12-31</th>\n",
       "      <td>1.304334</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2007-12-31</th>\n",
       "      <td>0.966593</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2008-12-31</th>\n",
       "      <td>-0.653941</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2009-12-31</th>\n",
       "      <td>0.799825</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2010-12-31</th>\n",
       "      <td>-0.143131</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2011-12-31</th>\n",
       "      <td>-0.216753</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2012-12-31</th>\n",
       "      <td>0.031695</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2013-12-31</th>\n",
       "      <td>-0.067493</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2014-12-31</th>\n",
       "      <td>0.528691</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2015-12-31</th>\n",
       "      <td>0.094136</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2016-12-31</th>\n",
       "      <td>-0.123062</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-12-31</th>\n",
       "      <td>0.065578</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2018-12-31</th>\n",
       "      <td>-0.245911</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2019-12-31</th>\n",
       "      <td>0.223032</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2020-12-31</th>\n",
       "      <td>0.138667</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2021-12-31</th>\n",
       "      <td>0.048001</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2022-12-31</th>\n",
       "      <td>-0.151250</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2023-12-31</th>\n",
       "      <td>-0.037007</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-12-31</th>\n",
       "      <td>0.121536</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            Raw_return\n",
       "Day                   \n",
       "1995-12-31   -0.142899\n",
       "1996-12-31    0.651425\n",
       "1997-12-31    0.302153\n",
       "1998-12-31   -0.039695\n",
       "1999-12-31    0.191750\n",
       "2000-12-31    0.517277\n",
       "2001-12-31   -0.206180\n",
       "2002-12-31   -0.175167\n",
       "2003-12-31    0.102670\n",
       "2004-12-31   -0.153997\n",
       "2005-12-31   -0.083253\n",
       "2006-12-31    1.304334\n",
       "2007-12-31    0.966593\n",
       "2008-12-31   -0.653941\n",
       "2009-12-31    0.799825\n",
       "2010-12-31   -0.143131\n",
       "2011-12-31   -0.216753\n",
       "2012-12-31    0.031695\n",
       "2013-12-31   -0.067493\n",
       "2014-12-31    0.528691\n",
       "2015-12-31    0.094136\n",
       "2016-12-31   -0.123062\n",
       "2017-12-31    0.065578\n",
       "2018-12-31   -0.245911\n",
       "2019-12-31    0.223032\n",
       "2020-12-31    0.138667\n",
       "2021-12-31    0.048001\n",
       "2022-12-31   -0.151250\n",
       "2023-12-31   -0.037007\n",
       "2024-12-31    0.121536"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Year_data = data_new.resample('YE')['Raw_return'].apply(lambda x: np.prod(1+x)-1).to_frame()\n",
    "Year_data"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "97e64dd0",
   "metadata": {},
   "source": [
    "## 计算均值(Mean)\n",
    "**算数平均值的公式：**\n",
    "$$A_n=\\frac{a_1+a_2+a_3+\\cdots+a_n}{n}$$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "id": "653abd08",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "np.float64(0.00026)"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "round(data_new['2000-01':'2024-09']['Raw_return'].mean(),5)\n",
    "# 选取2000年1月至2024年9月的日原始收益率数据\n",
    "# 调用Pandas的mean()方法，计算该时间段内收益率的均值。\n",
    "# 用round()函数将结果保留5位小数。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "id": "a2dbc5c3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "np.float64(0.0002576419497498928)"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\n",
    "np.mean(data_new['2000-01':'2024-09']['Raw_return'])\n",
    "# 调用NumPy的mean()函数计算均值.\n",
    "# 注意两段代码的书写逻辑: NumPy在数值计算的通用性和性能上有一定优势，与Pandas的mean()方法功能一致但属于不同库的实现。"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c6e77915",
   "metadata": {},
   "source": [
    "·收益率均值输出"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "id": "81ab8cc7",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "中国股票市场日度平均收益率为0.026%\n"
     ]
    }
   ],
   "source": [
    "print('中国股票市场日度平均收益率为',data_new['2000-01':'2024-09']['Raw_return'].mean().round(5)*100,'%',sep=\"\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "id": "f212c36b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "中国股票市场月度平均收益率为0.6%\n"
     ]
    }
   ],
   "source": [
    "print('中国股票市场月度平均收益率为',Month_data['2000-01':'2024-09']['Raw_return'].mean().round(3)*100,'%',sep=\"\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "id": "6c2070fd",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "中国股票市场年度平均收益率为10.74%\n"
     ]
    }
   ],
   "source": [
    "print('中国股票市场年度平均收益率为',Year_data['2000':'2024']['Raw_return'].mean().round(5)*100,'%',sep=\"\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e1778f5e",
   "metadata": {},
   "source": [
    "·均值计算"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "id": "bb0bae0d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0002576419497498928"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sum(data_new['2000-01':'2024-09']['Raw_return']) / len(data_new['2000-01':'2024-09']['Raw_return'])\n",
    "#  用均值计算的底层逻辑：“求和/样本量”，验证 Pandasmean()方法的结果，"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "id": "bfa46336",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "count    7223.000000\n",
       "mean        0.000362\n",
       "std         0.016464\n",
       "min        -0.163937\n",
       "25%        -0.006719\n",
       "50%         0.000468\n",
       "75%         0.007570\n",
       "max         0.309870\n",
       "Name: Raw_return, dtype: float64"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data_new['1995-01':'2024-09']['Raw_return'].describe()\n",
    "# 对1995年1月至2024年9月的日收益率数据执行describe方法。\n",
    "# 可输出均值、标准差、最小值、最大值、四分位数等统计指标，全面刻画收益率的分布特征。"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0eb2bcbb",
   "metadata": {},
   "source": [
    "## 分位数\n",
    "·分位数（Quantile），亦称分位点，是指将一个随机变量的概率分布范围分为几个等份的数值点，常用的有中位数（即二分位数）、四分位数、百分位数等。分位数。"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9943f250",
   "metadata": {},
   "source": [
    "举例子，我们班上有10名同学，他们的期末成绩是【20，24，38，34，43，56，76，86，98，100】\n",
    "如果期末考试要让40%的不通过，60%的人通过，分数线是多少呢？"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "12b49565",
   "metadata": {},
   "source": [
    "常见的分类方法：\n",
    "\n",
    "- 中位数 Median\n",
    "  - 当N是奇数时\n",
    "    - $$m_{0.5}=X_{(N+1) / 2}$$\n",
    "  - 当N是偶数时\n",
    "    - $$m_{0.5}=\\frac{X_{(N / 2)}+X_{(N / 2+1)}}{2}$$\n",
    "- 四分位数 Quartile\n",
    "- 10分位数 常用在股票投资策略中"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "90d2c823",
   "metadata": {},
   "source": [
    "一些q分位数有特殊名称：\n",
    "- 唯一的2分位数称为**中位数**\n",
    "- 3分位数称为**三分位数**（tertiles 或 terciles）\n",
    "- 4分位数称为**四分位数**（quartiles）\n",
    "- 5分位数称为**五分位数**（quintiles）\n",
    "- 6分位数称为**六分位数**（sextiles）\n",
    "- 7分位数称为**七分位数**（septiles）\n",
    "- 8分位数称为**八分位数**（octiles）\n",
    "- 10分位数称为**十分位数**（deciles）\n",
    "- 12分位数称为**十二分位数**（duo-deciles 或 dodeciles）\n",
    "- 16分位数称为**十六分位数**（hexadeciles）\n",
    "- 20分位数称为**二十分位数**（ventiles、vigintiles 或 demi-deciles）\n",
    "- 100分位数称为**百分位数**（percentiles）"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "id": "d652898c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "7223"
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(data_new['1995-01':'2024-09'])\n",
    "# 统计data_new中1995年1月至2024年9月这段时间内的数据行数"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "id": "cd26b850",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3775"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(data_new[data_new[\"Raw_return\"] > 0])\n",
    "# 统计data_new数据集中 “Raw_return”（原始收益率）大于 0 的条目数量"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "id": "98305828",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.5226360238128201"
      ]
     },
     "execution_count": 67,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(data_new[data_new[\"Raw_return\"] > 0])/len(data_new)\n",
    "# 计算数据集中 “Raw_return”（原始收益率）大于0的条目占总条目的比例"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "id": "ef26a4af",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[-0.01627982595925277,\n",
       " -0.00891266760735836,\n",
       " -0.004910564933516537,\n",
       " -0.0019116496227742363,\n",
       " 0.0004683483640481878,\n",
       " 0.002848688258116505,\n",
       " 0.005774506385657308,\n",
       " 0.009791348801684752,\n",
       " 0.017195204716027]"
      ]
     },
     "execution_count": 68,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from statistics import quantiles\n",
    "# 从statistics模块导入quantiles函数，对1995年1月至2024年9月的原始收益率计算10分位数。\n",
    "# 采用method='exclusive'的计算逻辑，该方法对数据端点的包含规则与inclusive不同，会影响分位数的具体结果。\n",
    "quantiles(data_new['1995-01':'2024-09']['Raw_return'], n = 10, method='exclusive')\n",
    "# 参数需要注意"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "id": "9c3bb599",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[-0.016273486796843283,\n",
       " -0.008904480681335824,\n",
       " -0.0049105335359804995,\n",
       " -0.0019112410821794379,\n",
       " 0.0004683483640481878,\n",
       " 0.0028484509548271308,\n",
       " 0.005764948233341815,\n",
       " 0.009789313259894784,\n",
       " 0.017182938215153553]"
      ]
     },
     "execution_count": 69,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "quantiles(data_new['1995-01':'2024-09']['Raw_return'], n = 10, method='inclusive')\n",
    "# 算1995年1月至2024年9月期间日原始收益率的十分位数"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "id": "964c47a5",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Help on function quantiles in module statistics:\n",
      "\n",
      "quantiles(data, *, n=4, method='exclusive')\n",
      "    Divide *data* into *n* continuous intervals with equal probability.\n",
      "\n",
      "    Returns a list of (n - 1) cut points separating the intervals.\n",
      "\n",
      "    Set *n* to 4 for quartiles (the default).  Set *n* to 10 for deciles.\n",
      "    Set *n* to 100 for percentiles which gives the 99 cuts points that\n",
      "    separate *data* in to 100 equal sized groups.\n",
      "\n",
      "    The *data* can be any iterable containing sample.\n",
      "    The cut points are linearly interpolated between data points.\n",
      "\n",
      "    If *method* is set to *inclusive*, *data* is treated as population\n",
      "    data.  The minimum value is treated as the 0th percentile and the\n",
      "    maximum value is treated as the 100th percentile.\n",
      "\n"
     ]
    }
   ],
   "source": [
    "import statistics\n",
    "# 导入Python标准库中的statistics模块，该模块提供了统计计算功能。\n",
    "help(statistics.quantiles)\n",
    "# 查看statistics.quantiles函数的详细说明，包括函数的参数、返回值、使用方法等信息。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "id": "9e5bea65",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[2.75, 5.5, 8.25]\n"
     ]
    }
   ],
   "source": [
    "data = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]\n",
    "q = statistics.quantiles(data, n=4, method='exclusive')\n",
    "print(q)\n",
    "# 首先定义了一个包含 1 到 10 的列表data。\n",
    "# 使用statistics模块的quantiles函数对data计算四分位数（n=4），方法为exclusive（排他性分位数计算方法）。\n",
    "# 打印计算得到的四分位数结果，用于展示不同分位数计算方法的差异。\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "id": "efc9d833",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[3.25, 5.5, 7.75]\n"
     ]
    }
   ],
   "source": [
    "q = statistics.quantiles(data, n=4, method='inclusive')\n",
    "# 同样对列表data计算四分位数，方法改为inclusive（包容性分位数计算方法）\n",
    "print(q)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "id": "0a20ecac",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "count    297.000000\n",
       "mean       0.005530\n",
       "std        0.070834\n",
       "min       -0.246314\n",
       "25%       -0.037767\n",
       "50%        0.004454\n",
       "75%        0.043145\n",
       "max        0.274464\n",
       "Name: Raw_return, dtype: float64"
      ]
     },
     "execution_count": 73,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Month_data['2000-01':'2024-09']['Raw_return'].describe()\n",
    "# 对Month_data中2000年1月至2024年9月的“Raw_return（月度收益率）”列执行describe()方法。\n",
    "# 该方法会输出均值、标准差、最小值、最大值、四分位数等统计指标，为分析中国股票市场月度收益的集中趋势和波动性提供基础统计信息。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "id": "17e00ff5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[-0.07509951200338086,\n",
       " -0.049078970439670154,\n",
       " -0.02727551483190027,\n",
       " -0.007864077660500212,\n",
       " 0.004295591179114044,\n",
       " 0.01985114557399421,\n",
       " 0.036354767176530745,\n",
       " 0.05593115044063066,\n",
       " 0.10336924547079081]"
      ]
     },
     "execution_count": 74,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "statistics.quantiles(Month_data['Raw_return'], n = 10, method='exclusive')\n",
    "# 计算十分位数（n=10），方法为exclusive。\n",
    "# 用于精细分析月度收益率在10个分位区间的分布情况，可探究收益的尾部特征等，为金融市场分析提供更细致的统计依据。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "id": "b7d0cc59",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.5266106442577031"
      ]
     },
     "execution_count": 75,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(Month_data['1995-01':'2024-09'][Month_data[\"Raw_return\"] > 0])/len(Month_data['1995-01':'2024-09'])\n",
    "# 计算月度收益率为正的频率，反映中国股票市场在这段时间内月度收益为正的概率，衡量市场表现。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "id": "de69512e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[-0.06864738437339708,\n",
       " -0.04812792871751108,\n",
       " -0.0256577261430311,\n",
       " -0.006190944913624752,\n",
       " 0.004453785546283395,\n",
       " 0.018812575594151015,\n",
       " 0.035870471048765264,\n",
       " 0.052147828136706396,\n",
       " 0.08994844112131037]"
      ]
     },
     "execution_count": 76,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "quantiles(Month_data['2000-01':'2024-09']['Raw_return'], n = 10, method='exclusive')\n",
    "# 计算十分位数，方法为exclusive。\n",
    "# 聚焦2000年后的月度收益率数据，分析该时间段内收益的分位分布特征，可对比不同时间段的市场收益分布差异，为研究市场阶段性表现提供统计支持。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "id": "65950929",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0. , 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1. ])"
      ]
     },
     "execution_count": 77,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "seq = np.linspace(0,1,11)\n",
    "# 使用NumPy的linspace函数生成一个从0到 1、包含11个元素的等间隔序列seq，这些数值代表分位数的位置\n",
    "seq\n",
    "# 执行该语句可查看生成的分位数序列，为后续分位数计算提供输入。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "id": "e9219d7d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-0.08840689, -0.01536682, -0.00833553, -0.00468863, -0.00176721,\n",
       "        0.00049848,  0.00268087,  0.00538043,  0.00914657,  0.01601642,\n",
       "        0.09856839])"
      ]
     },
     "execution_count": 78,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.quantile(data_new['2000-01':'2024-09']['Raw_return'],q=seq)\n",
    "# 选取2000年1月至2024年9月的日原始收益率数据。\n",
    "# 以seq为分位数位置参数，计算对应的多个分位数，用于全面分析日收益率在不同分位区间的分布情况。"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9a47c011",
   "metadata": {},
   "source": [
    "## 波动率 Variance"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ba036e51",
   "metadata": {},
   "source": [
    "$$\\sigma^2=\\frac{\\sum(X-\\mu)^2}{N}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2b4d40f6",
   "metadata": {},
   "source": [
    "$$ R_{t+1} = a + b * VAR_t $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "id": "682e1f61",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.00021706077602811542"
      ]
     },
     "execution_count": 79,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.var(data_new['2000-01':'2024-09']['Raw_return'])\n",
    "# 调用 NumPy 的var函数，计算data_new中2000年1月至2024年9月“Raw_return（日原始收益率）”的方差"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "id": "d546706b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.00021706077602811545"
      ]
     },
     "execution_count": 80,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m = np.mean(data_new['2000-01':'2024-09']['Raw_return'])\n",
    "sum((data_new['2000-01':'2024-09']['Raw_return'] - m)**2) / len(data_new['2000-01':'2024-09']['Raw_return'])\n",
    "# 通过np.mean计算日收益率的均值m，再通过“平方差和/样本量”的公式手动计算方差，用于验证NumPyvar函数的结果"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "id": "1c568b2f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.014732982591047728"
      ]
     },
     "execution_count": 81,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.std(data_new['2000-01':'2024-09']['Raw_return'])\n",
    "# 调用 NumPy 的std函数，计算日收益率的标准差"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "id": "83429e45",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "np.float64(0.014732982591047728)"
      ]
     },
     "execution_count": 82,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sqrt(np.var(data_new['2000-01':'2024-09']['Raw_return']))\n",
    "# 先通过np.var计算方差，再用NumPy的sqrt函数求平方根，得到标准差。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "id": "f2be8cc5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.014732982591047728"
      ]
     },
     "execution_count": 83,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from math import sqrt\n",
    "sqrt(np.var(data_new['2000-01':'2024-09']['Raw_return']))\n",
    "# 从Python标准库math中导入sqrt函数，对np.var计算得到的方差求平方根，得到标准差。"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7e10e87b",
   "metadata": {},
   "source": [
    "# 作业\n",
    "计算每个月的波动率——方差。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "id": "89d2bdb8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
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       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
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       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Variance</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Day</th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1995-01-31</th>\n",
       "      <td>0.000260</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1995-02-28</th>\n",
       "      <td>0.001130</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1995-03-31</th>\n",
       "      <td>0.000551</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1995-04-30</th>\n",
       "      <td>0.000407</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1995-05-31</th>\n",
       "      <td>0.006924</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-05-31</th>\n",
       "      <td>0.000048</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-06-30</th>\n",
       "      <td>0.000031</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-07-31</th>\n",
       "      <td>0.000065</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-08-31</th>\n",
       "      <td>0.000031</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-09-30</th>\n",
       "      <td>0.000533</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>357 rows × 1 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "            Variance\n",
       "Day                 \n",
       "1995-01-31  0.000260\n",
       "1995-02-28  0.001130\n",
       "1995-03-31  0.000551\n",
       "1995-04-30  0.000407\n",
       "1995-05-31  0.006924\n",
       "...              ...\n",
       "2024-05-31  0.000048\n",
       "2024-06-30  0.000031\n",
       "2024-07-31  0.000065\n",
       "2024-08-31  0.000031\n",
       "2024-09-30  0.000533\n",
       "\n",
       "[357 rows x 1 columns]"
      ]
     },
     "execution_count": 84,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "monthly_var = data_new.resample('ME')['Raw_return'].var().to_frame()\n",
    "monthly_var.rename(columns={'Raw_return':'Variance'},inplace=True)\n",
    "monthly_var"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a6e84cb6",
   "metadata": {},
   "source": [
    "·下面是对上面那段代码的改进: 添加标准差计算与列重命名"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "id": "be0a78e8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
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       "\n",
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       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Variance</th>\n",
       "      <th>Std_Dev</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Day</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1995-01-31</th>\n",
       "      <td>0.000260</td>\n",
       "      <td>0.016140</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1995-02-28</th>\n",
       "      <td>0.001130</td>\n",
       "      <td>0.033609</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1995-03-31</th>\n",
       "      <td>0.000551</td>\n",
       "      <td>0.023470</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1995-04-30</th>\n",
       "      <td>0.000407</td>\n",
       "      <td>0.020169</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1995-05-31</th>\n",
       "      <td>0.006924</td>\n",
       "      <td>0.083211</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-05-31</th>\n",
       "      <td>0.000048</td>\n",
       "      <td>0.006935</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-06-30</th>\n",
       "      <td>0.000031</td>\n",
       "      <td>0.005586</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-07-31</th>\n",
       "      <td>0.000065</td>\n",
       "      <td>0.008084</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-08-31</th>\n",
       "      <td>0.000031</td>\n",
       "      <td>0.005588</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-09-30</th>\n",
       "      <td>0.000533</td>\n",
       "      <td>0.023095</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>357 rows × 2 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "            Variance   Std_Dev\n",
       "Day                           \n",
       "1995-01-31  0.000260  0.016140\n",
       "1995-02-28  0.001130  0.033609\n",
       "1995-03-31  0.000551  0.023470\n",
       "1995-04-30  0.000407  0.020169\n",
       "1995-05-31  0.006924  0.083211\n",
       "...              ...       ...\n",
       "2024-05-31  0.000048  0.006935\n",
       "2024-06-30  0.000031  0.005586\n",
       "2024-07-31  0.000065  0.008084\n",
       "2024-08-31  0.000031  0.005588\n",
       "2024-09-30  0.000533  0.023095\n",
       "\n",
       "[357 rows x 2 columns]"
      ]
     },
     "execution_count": 85,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 计算月度方差和标准差\n",
    "monthly_vol = data_new.resample('ME')['Raw_return'].agg(['var', 'std'])\n",
    "# 重命名列，提升可读性\n",
    "monthly_vol.rename(columns={'var':'Variance', 'std':'Std_Dev'}, inplace=True)\n",
    "monthly_vol"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "id": "74ed0483",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
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       "\n",
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       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Variance</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Day</th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1995-01-31</th>\n",
       "      <td>0.005695</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1995-02-28</th>\n",
       "      <td>0.018086</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1995-03-31</th>\n",
       "      <td>0.013378</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1995-04-30</th>\n",
       "      <td>0.008281</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1995-05-31</th>\n",
       "      <td>0.148387</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-05-31</th>\n",
       "      <td>0.000915</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-06-30</th>\n",
       "      <td>0.000642</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-07-31</th>\n",
       "      <td>0.001441</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-08-31</th>\n",
       "      <td>0.000705</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-09-30</th>\n",
       "      <td>0.011045</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>357 rows × 1 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "            Variance\n",
       "Day                 \n",
       "1995-01-31  0.005695\n",
       "1995-02-28  0.018086\n",
       "1995-03-31  0.013378\n",
       "1995-04-30  0.008281\n",
       "1995-05-31  0.148387\n",
       "...              ...\n",
       "2024-05-31  0.000915\n",
       "2024-06-30  0.000642\n",
       "2024-07-31  0.001441\n",
       "2024-08-31  0.000705\n",
       "2024-09-30  0.011045\n",
       "\n",
       "[357 rows x 1 columns]"
      ]
     },
     "execution_count": 86,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data_new[\"Return_2\"] = data_new[\"Raw_return\"]**2\n",
    "monthly_var = data_new.resample('ME')['Return_2'].sum().to_frame()\n",
    "monthly_var.rename(columns={'Return_2':'Variance'},inplace=True)\n",
    "monthly_var"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "58c260c9",
   "metadata": {},
   "source": [
    "·精进后的代码：合并步骤，简化逻辑"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "id": "886c48f4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Raw_return</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Day</th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1995-01-31</th>\n",
       "      <td>0.005695</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1995-02-28</th>\n",
       "      <td>0.018086</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1995-03-31</th>\n",
       "      <td>0.013378</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1995-04-30</th>\n",
       "      <td>0.008281</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1995-05-31</th>\n",
       "      <td>0.148387</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-05-31</th>\n",
       "      <td>0.000915</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-06-30</th>\n",
       "      <td>0.000642</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-07-31</th>\n",
       "      <td>0.001441</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-08-31</th>\n",
       "      <td>0.000705</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-09-30</th>\n",
       "      <td>0.011045</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>357 rows × 1 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "            Raw_return\n",
       "Day                   \n",
       "1995-01-31    0.005695\n",
       "1995-02-28    0.018086\n",
       "1995-03-31    0.013378\n",
       "1995-04-30    0.008281\n",
       "1995-05-31    0.148387\n",
       "...                ...\n",
       "2024-05-31    0.000915\n",
       "2024-06-30    0.000642\n",
       "2024-07-31    0.001441\n",
       "2024-08-31    0.000705\n",
       "2024-09-30    0.011045\n",
       "\n",
       "[357 rows x 1 columns]"
      ]
     },
     "execution_count": 87,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 直接通过聚合函数计算月度收益率平方和（即方差，假设均值为0的简化场景，若需精确方差需结合均值调整，此处原逻辑是简化版）\n",
    "monthly_var = data_new.resample('ME')['Raw_return'].apply(lambda x: (x**2).sum()).to_frame().rename(columns={0:'Variance'})\n",
    "monthly_var"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8068a1f6",
   "metadata": {},
   "source": [
    "# 正态分布"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "099b3340",
   "metadata": {},
   "source": [
    "若随机变量X服从一个数学期望为 $\\mu$ 、方差为 $\\sigma^{2}$ 的正态分布，记为 $\\mathrm{N}\\left(\\mu, \\sigma^{2}\\right)$ 。其概率密度函数为正态分布的期望值决定了 其位置，其标准差$\\sigma$决定了分布的幅度。当 $\\mu=0, \\sigma=1$ 时的正态分布是标准正态分布。\n",
    "\n",
    "若随机变量 $X$ 服从一个位置参数为 $\\mu$ 、尺度参数为 $\\sigma$ 的概率分布，且其概率密度函数为 \n",
    "$$\n",
    "f(x)=\\frac{1}{\\sqrt{2 \\pi} \\sigma} \\exp \\left(-\\frac{(x-\\mu)^{2}}{2 \\sigma^{2}}\\right)\n",
    "$$\n",
    "则这个随机变量就称为正态随机变量, 正态随机变量服从的分布就称为正态分布, 记作 $X \\sim N\\left(\\mu, \\sigma^{2}\\right)$, 读作 $X$ 服从 $N\\left(\\mu, \\sigma^{2}\\right)$, 或 $X$ 服从正态分布。\n",
    "\n",
    " 若 $X \\sim N\\left(\\mu, \\sigma^{2}\\right), Y=\\frac{X-\\mu}{\\sigma} \\sim N(0,1)$.\n",
    " \n",
    " 当 $\\mu=0, \\sigma=1$ 时，正态分布就成为标准正态分布\n",
    "$$\n",
    "f(x)=\\frac{1}{\\sqrt{2 \\pi}} e^{\\left(-\\frac{x^{2}}{2}\\right)}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "efb5588b",
   "metadata": {},
   "source": [
    "# 偏度和峰度"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "id": "76737d61",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "7223"
      ]
     },
     "execution_count": 88,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "np.float64(0.7024696049464008)"
      ]
     },
     "execution_count": 88,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "np.float64(23.472220480449483)"
      ]
     },
     "execution_count": 88,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "np.float64(23.455144815692734)"
      ]
     },
     "execution_count": 88,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "np.float64(23.455144815692734)"
      ]
     },
     "execution_count": 88,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Daily data\n",
    "len(data_new['1995-01':'2024-09'])\n",
    "# 计算data_new中1995年1月至2024年9月期间数据的样本数量\n",
    "data_new['1995-01':'2024-09']['Raw_return'].skew()\n",
    "# 计算偏度\n",
    "data_new['1995-01':'2024-09']['Raw_return'].kurt()\n",
    "# 计算峰度\n",
    "scipy.stats.kurtosis(data_new['1995-01':'2024-09']['Raw_return'],fisher=False) - 3\n",
    "# 计算绝对峰度\n",
    "scipy.stats.kurtosis(data_new['1995-01':'2024-09']['Raw_return'],fisher=True)\n",
    "# 计算超额峰度"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "id": "e1810496",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "23.45514481569284"
      ]
     },
     "execution_count": 89,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m = np.mean(data_new['1995-01':'2024-09']['Raw_return'])\n",
    "# 计算均值，并赋值给变量m\n",
    "l = len(data_new['1995-01':'2024-09']['Raw_return'])\n",
    "# 计算样本数量，并赋值给变量l\n",
    "sum(((data_new['1995-01':'2024-09']['Raw_return'] - m)/np.std(data_new['1995-01':'2024-09']['Raw_return']))**4) / l -3\n",
    "# 手动计算日收益率的超额峰度\n",
    "# 对每个收益率数据“（数据-均值）/标准差”的标准化处理，再对标准化后的值取4次方，求和后除以样本量l，最后减3\n",
    "# （正态分布的绝对峰度为 3，此处计算超额峰度）"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "id": "72370629",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "np.float64(0.32934252744736264)"
      ]
     },
     "execution_count": 90,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "np.float64(1.9091672959136194)"
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     },
     "execution_count": 90,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Monthly data\n",
    "Month_data['1995-01':'2024-09']['Raw_return'].skew()\n",
    "# 算偏度\n",
    "Month_data['1995-01':'2024-09']['Raw_return'].kurt()\n",
    "# 算超额峰度"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "id": "7e2be1fc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "np.float64(0.8675024485714982)"
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     },
     "execution_count": 91,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "np.float64(1.7137615374448099)"
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     },
     "execution_count": 91,
     "metadata": {},
     "output_type": "execute_result"
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   ],
   "source": [
    "# Quarterly data\n",
    "Quarter_data['1995-01':'2024-09']['Raw_return'].skew()\n",
    "# 算偏度\n",
    "Quarter_data['1995-01':'2024-09']['Raw_return'].kurt()\n",
    "# 算超额峰度"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e1540ef2",
   "metadata": {},
   "source": [
    "# 标准正态分布的直方图"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "id": "906142d1",
   "metadata": {},
   "outputs": [
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    "# 根据均值、标准差,求指定范围的正态分布概率值\n",
    "\n",
    "'''\"\n",
    "normfun(x, mu, sigma) 函数定义了一个正态分布的概率密度函数，\n",
    "其中 x 是自变量\n",
    "mu 是均值\n",
    "sigma 是标准差\n",
    "这个函数计算了在给定均值和标准差下 x 处的概率密度值。\n",
    "'''\n",
    "\n",
    "def normfun(x, mu, sigma):\n",
    "  pdf = np.exp(-((x - mu)**2)/(2*sigma**2)) / (sigma * np.sqrt(2*np.pi))\n",
    "  return pdf\n",
    "\n",
    "\n",
    "# 生成高斯分布的概率密度随机数\n",
    "result = np.random.normal(0, 1, 1000000) # mean 0 and standard deviation 1\n",
    "\n",
    "# np.arange()\n",
    "# 函数返回一个有终点和起点的固定步长的排列，如[1,2,3,4,5]，起点是1，终点是6，步长为1。\n",
    "# 参数个数情况： np.arange()函数分为一个参数，两个参数，三个参数三种情况\n",
    "# 1）一个参数时，参数值为终点，起点取默认值0，步长取默认值1。\n",
    "# 2）两个参数时，第一个参数为起点，第二个参数为终点，步长取默认值1。\n",
    "# 3）三个参数时，第一个参数为起点，第二个参数为终点，第三个参数为步长。其中步长支持小数\n",
    "\n",
    "x = np.arange(min(result), max(result),0.01)\n",
    "\n",
    "# 设定 y 轴，载入刚才的正态分布函数\n",
    "y = normfun(x, result.mean(), result.std())\n",
    "plt.plot(x, y) # 这里画出理论的正态分布概率曲线\n",
    " \n",
    "# 这里画出实际的参数概率与取值关系\n",
    "fig = plt.hist(result, bins=100, rwidth=1, density=True) # bins=100 表示将数据分成100个柱状图，density=True 表示将频率转换为概率密度。宽度是rwidth(0~1),=1没有缝隙\n",
    "plt.title('distribution')\n",
    "#plt.xlabel('')\n",
    "plt.ylabel('probability')\n",
    "# 输出\n",
    "plt.show(); # 最后图片的概率和不为1是因为正态分布是从负无穷到正无穷,这里指截取了数据最小值到最大值的分布"
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  {
   "cell_type": "markdown",
   "id": "4dc457bd",
   "metadata": {},
   "source": [
    "下面是对前面生成图像代码的改进，改进点：将逻辑封装为函数，支持自定义均值、标准差、样本量等参数，明确区分理论曲线和实际分布的可视化样式，添加了图例增强可读性。"
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  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "id": "13de6cda",
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   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "def plot_normal_distribution(mu=0, sigma=1, n_samples=1000000, bins=100, title='Normal Distribution'):\n",
    "    # 生成正态分布随机数\n",
    "    result = np.random.normal(mu, sigma, n_samples)\n",
    "    # 定义正态分布概率密度函数\n",
    "    def normfun(x, mu, sigma):\n",
    "        return np.exp(-((x - mu)**2)/(2*sigma**2)) / (sigma * np.sqrt(2*np.pi))\n",
    "    # 生成x轴数据\n",
    "    x = np.arange(min(result), max(result), 0.01)\n",
    "    # 计算理论概率密度\n",
    "    y = normfun(x, mu, sigma)\n",
    "    # 绘图\n",
    "    plt.figure(figsize=(10, 6))\n",
    "    # 绘制理论曲线\n",
    "    plt.plot(x, y, color='red', label='Theoretical PDF')\n",
    "    # 绘制实际直方图（概率密度形式）\n",
    "    plt.hist(result, bins=bins, rwidth=0.9, density=True, alpha=0.6, label='Empirical Distribution')\n",
    "    plt.title(title)\n",
    "    plt.xlabel('Value')\n",
    "    plt.ylabel('Probability Density')\n",
    "    plt.legend()\n",
    "    plt.show()\n",
    "\n",
    "# 调用示例\n",
    "plot_normal_distribution(mu=0, sigma=1, title='Standard Normal Distribution')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fd6bb626",
   "metadata": {},
   "source": [
    "# 在日收益率直方图上添加正态分布密度曲线"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "id": "9e002010",
   "metadata": {},
   "outputs": [
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   "source": [
    "retmean = data_new['2000-01':'2024-09']['Raw_return'].mean()\n",
    "# 计算data_new中2000年1月至2024年9月期间“Raw_return（日原始收益率）”的均值，并将结果赋值给retmean。\n",
    "retstd = data_new['2000-01':'2024-09']['Raw_return'].std()\n",
    "retmin = data_new['2000-01':'2024-09']['Raw_return'].min()\n",
    "retmax = data_new['2000-01':'2024-09']['Raw_return'].max()\n",
    "\n",
    "\n",
    "def normfun(x, mu, sigma):\n",
    "    pdf = np.exp(-((x - mu)**2) /\n",
    "                 (2 * sigma**2)) / (sigma * np.sqrt(2 * np.pi))\n",
    "    return pdf\n",
    "\n",
    "# 定义了一个用于计算正态分布概率密度的函数normfun。其中，x是自变量，mu是均值，sigma是标准差。\n",
    "# 函数内部通过正态分布的概率密度公式计算给定x处的概率密度值pdf，该公式是正态分布的数学表达式，用于后续绘制理论正态分布曲线。\n",
    "\n",
    "x = np.arange(retmin, retmax, 0.001) # 0.001 0.002 0.003 0.004.。。。 0.099 0.100  0.101\n",
    "y = normfun(x, retmean, retstd)\n",
    "fig = plt.figure(figsize=(10, 5))\n",
    "plt.plot(x, y)\n",
    "\n",
    "fig = plt.hist(data_new['2000-01':'2024-09']['Raw_return'], # index daily market excess return\n",
    "               bins=1000,\n",
    "               histtype='bar',\n",
    "               color='r',\n",
    "               alpha=0.9)\n",
    "# bins=1000表示将数据分成1000个区间，使直方图能精细展示收益率的分布；\n",
    "# histtype='bar'指定直方图类型为柱状图；color='r'设置柱子颜色为红色；alpha=0.9调整柱子的透明度，便于与理论正态分布曲线对比。\n",
    "plt.xticks(rotation=90, fontsize=8) # x轴显示方法\n",
    "plt.title('Distribution')\n",
    "plt.xlabel('Market Return From January 2000 to September 2024')\n",
    "plt.ylabel('Probability')\n",
    "plt.show();"
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  },
  {
   "cell_type": "markdown",
   "id": "7dac4df4",
   "metadata": {},
   "source": [
    "# 在月收益率直方图上添加正态分布密度曲线"
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      ],
      "text/plain": [
       "<Figure size 1000x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "retmean = Month_data['2000-01':'2024-09']['Raw_return'].mean()\n",
    "retstd = Month_data['2000-01':'2024-09']['Raw_return'].std()\n",
    "retmin = Month_data['2000-01':'2024-09']['Raw_return'].min()\n",
    "retmax = Month_data['2000-01':'2024-09']['Raw_return'].max()\n",
    "\n",
    "\n",
    "def normfun(x, mu, sigma):\n",
    "    pdf = np.exp(-((x - mu)**2) /\n",
    "                 (2 * sigma**2)) / (sigma * np.sqrt(2 * np.pi))\n",
    "    return pdf\n",
    "\n",
    "\n",
    "x = np.arange(retmin, retmax, 0.001)\n",
    "y = normfun(x, retmean, retstd)\n",
    "fig = plt.figure(figsize=(10, 5)) # 图片大小 10，5\n",
    "plt.plot(x, y)\n",
    "\n",
    "fig = plt.hist(Month_data['2000-01':'2024-09']['Raw_return'],\n",
    "               bins=100,\n",
    "               histtype='bar',\n",
    "               color='r',\n",
    "               alpha=0.9)\n",
    "plt.xticks(rotation=90, fontsize=8)\n",
    "plt.title('Distribution')\n",
    "plt.xlabel('Market Return From January 2000 to December 2023')\n",
    "plt.ylabel('Probability')\n",
    "plt.show();"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "58e7bb1a",
   "metadata": {},
   "source": [
    "# 平稳性 stationary\n",
    "没有时间趋势"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "id": "22802c7c",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "原始序列的ADF检验结果为: (np.float64(-6.073484496717496), np.float64(1.136086777178037e-07), 13, 283, {'1%': np.float64(-3.453670163592738), '5%': np.float64(-2.8718077069772248), '10%': np.float64(-2.5722411158835796)}, np.float64(-690.35040034144))\n"
     ]
    }
   ],
   "source": [
    "from statsmodels.tsa.stattools import adfuller as ADF\n",
    "# 从statsmodels库的时间序列工具模块中导入adfuller函数，并为其设置别名ADF。\n",
    "# adfuller是实现Augmented Dickey-Fuller（ADF）检验的核心函数，用于判断时间序列是否具有平稳性。\n",
    "print('原始序列的ADF检验结果为:', ADF(Month_data['2000-01':'2024-09']['Raw_return']))"
   ]
  }
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